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Everything about Hyperbolic functions

Hyperbolic analogues of trigonometric functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t), the derivatives of sinh(t) and cosh(t) are cosh(t) and sinh(t). Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Hyperbolic functionsA 5-minute orientation
  2. Skim a recent paper: Hyperbolic metamaterials: fusing artificial structures to natural 2D materialsInfluential work since 2022
  3. Pick up a classic book: Omega tableThe most-reprinted book on the subject
  4. Read the landmark paper: Golden Eggs and Hyperbolic DiscountingCited 4,204 times
  5. Go sideways: Trigonometric functionsA closely related topic
  6. Go sideways: Hyperbolic triangleA closely related topic

📖 Definitions

Adjective Of or relating to hyperbole.

Adjective Using hyperbole: exaggerated.

Adjective Of a perceived color, having a saturation exceeding 100%.

Adjective Of or pertaining to a hyperbola.

🗂️ The subject at a glance

  1. History
  2. Notation
  3. Definitions
  4. Characterizing properties
  5. Useful relations
  6. Inverse functions as logarithms
  7. Derivatives
  8. Second derivatives
  9. Standard integrals
  10. Taylor series expressions
  11. Infinite products and continued fractions
  12. Comparison with circular functions

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics